This work is the second of a two-part research project focused on modeling solid-shell elements using a stabilized two-field finite element formulation. The first part introduces a stabilization technique based on the Variational Multiscale framework, which is proven to effectively address numerical locking in infinitesimal strain problems. The primary objective of the study was to characterize the inherent numerical locking effects of solid-shell elements in order to comprehensively understand their triggers and how stabilized mixed formulations can overcome them. In this current phase of the work, the concept is extended to finite strain solid dynamics involving hyperelastic materials. The aim of introducing this method is to obtain a robust stabilized mixed formulation that enhances the accuracy of the stress field. This improved formulation holds great potential for accurately approximating shell structures undergoing finite deformations. To this end, three techniques based in the Variational Multiscale stabilization framework are presented. These stabilized formulations allow circumventing the compatibility restriction of interpolating spaces of the unknowns inherent to mixed formulations, thus allowing any combination of them. The accuracy of the stress field is successfully enhanced while maintaining the accuracy of the displacement field. These improvements are also inherited to the solid-shell elements, providing locking-free approximation of thin structures.

中文翻译：

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使用实体壳单元对薄结构进行应力-位移稳定有限元分析，第二部分：有限应变超弹性


这项工作是由两部分组成的研究项目的第二部分，重点是使用稳定的双场有限元公式对实体壳单元进行建模。第一部分介绍了基于变分多尺度框架的稳定技术，该技术被证明可以有效解决无穷小应变问题中的数值锁定。该研究的主要目的是表征固壳单元固有的数值锁定效应，以便全面了解其触发因素以及稳定的混合配方如何克服它们。在当前阶段的工作中，该概念已扩展到涉及超弹性材料的有限应变固体动力学。引入该方法的目的是获得稳健的稳定混合配方，从而提高应力场的准确性。这种改进的公式对于精确近似经历有限变形的壳结构具有巨大的潜力。为此，提出了基于变分多尺度稳定框架的三种技术。这些稳定的配方可以规避混合配方固有的未知数插值空间的兼容性限制，从而允许它们的任意组合。在保持位移场精度的同时，成功提高了应力场的精度。这些改进也继承到了实体壳单元，提供了薄结构的无锁定近似。